Transformations and Projections in Computer Graphics


Book Description

This book introduces perspective, and discusses the mathematics of perspective in a detailed, yet accessible style. It also reviews nonlinear projections, including the fisheye, panorama, and map projections frequently used to enhance digital images. Topics and features include a complete and self-contained presentation of concepts, principles, and methods; a 12-page colour section, and numerous figures. This essential resource for computer professionals both within and outside the field of Computer Graphics is also suitable for graduates and advanced undergraduates in Computer Graphics and Computer-Aided Design. Key ideas are introduced, examined and illustrated by figures and examples, and reinforced through solved exercises.




Computer Graphics


Book Description

This book adopts a conceptual approach to computer graphics, with emphasis on mathematical concepts and their applications. It introduces an abstract paradigm that relates the mathematical concepts with computer graphic techniques and implementation methods. This model is intended to help the reader understand the mathematical concepts and their practical use. However, mathematical complexity has not been allowed to dominate. The haul mark of the book is its profuse solved examples which aid in the understanding of mathematical concepts. The text is supplemented with introduction to various graphics standards, animation, multimedia techniques and fractals. These topics are of immense use in each of the three visual disciplines: modeling transformations, projections and multi-view geometry for computer vision. Geometry of lines, vectors and planes is essential for any geometric computation problem, light and illumination for image-based rendering, and hidden surface removal. Almost every chapter has the working source code to illustrate the concepts, which could be written and used as small programs for better understanding of the topics. A concise appendix of open source OpenGL is also included to showcase programming concepts of computer graphics and visualization. The text is completely platform-independent and the only prerequisite is the knowledge of coordinate geometry and basic algebra. It will be useful both as a text and reference, thus it can easily be used by novices and experienced practitioners alike.




Computer Graphics and Geometric Modeling


Book Description

A book for those interested in how modern graphics programs work and how they can generate realistic-looking objects. It emphasises the mathematics behind computer graphics, most of which is included in an appendix. The main topics covered are: scan conversion methods; selecting the best pixels for generating lines, circles and other objects; geometric transformations and projections; translations, rotations, moving in 3D, perspective projections, curves and surfaces; construction, wire-frames, rendering, normals; CRTs, antialiasing, animation, colour, perception, polygons, compression. With its numerous illustrative examples and exercises, the book is ideal for a two-semester course for advanced undergraduates or graduates, while also making a fine reference for professionals in the field.




Computer Graphics from Scratch


Book Description

Computer Graphics from Scratch demystifies the algorithms used in modern graphics software and guides beginners through building photorealistic 3D renders. Computer graphics programming books are often math-heavy and intimidating for newcomers. Not this one. Computer Graphics from Scratch takes a simpler approach by keeping the math to a minimum and focusing on only one aspect of computer graphics, 3D rendering. You’ll build two complete, fully functional renderers: a raytracer, which simulates rays of light as they bounce off objects, and a rasterizer, which converts 3D models into 2D pixels. As you progress you’ll learn how to create realistic reflections and shadows, and how to render a scene from any point of view. Pseudocode examples throughout make it easy to write your renderers in any language, and links to live JavaScript demos of each algorithm invite you to explore further on your own. Learn how to: Use perspective projection to draw 3D objects on a 2D plane Simulate the way rays of light interact with surfaces Add mirror-like reflections and cast shadows to objects Render a scene from any camera position using clipping planes Use flat, Gouraud, and Phong shading to mimic real surface lighting Paint texture details onto basic shapes to create realistic-looking objects Whether you’re an aspiring graphics engineer or a novice programmer curious about how graphics algorithms work, Gabriel Gambetta’s simple, clear explanations will quickly put computer graphics concepts and rendering techniques within your reach. All you need is basic coding knowledge and high school math. Computer Graphics from Scratch will cover the rest.




Visualization of Basic Transformations in Computer Graphics


Book Description

Transformations play a basic and key role in OpenGL and computer graphics. Basic transformations, which are represented by matrix multiplication, include modelling, viewing, and projection transformations. They involve rotations, translations, scalings, reflecting, orthographic and perspective projection. This report describes the design and implementation of visualization tool for basic transformations. First all, we describe basic transformations in OpenGL, such as viewing, modelling, projection, and viewport transformations. And we describe some ways to implement these transformations. Secondly, we give the detailed description of design and implementation based on the above specification. In the design stage, we consider the following transformations: viewing, modelling, and viewport transformations are called "model view"' and the "projection" transformation. In implementation stage, we implement coding depending on the above design, namely, "model view transformation" visualization and "projection transformation" visualization. Finally, we include user's guide, and some open problem.




Orthographic Projection


Book Description

What is Orthographic Projection Orthographic projection is a means of representing three-dimensional objects in two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are not orthogonal to the projection plane. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Orthographic projection Chapter 2: Orthogonal matrix Chapter 3: Isometric projection Chapter 4: Engineering drawing Chapter 5: 3D projection Chapter 6: Axonometric projection Chapter 7: Descriptive geometry Chapter 8: Oblique projection Chapter 9: Parallel projection Chapter 10: Axonometry (II) Answering the public top questions about orthographic projection. (III) Real world examples for the usage of orthographic projection in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Orthographic Projection.







Computer Graphics and Imaging


Book Description

Computer graphics development is so quick that it has expanded from devices designed for military and top industrial applications to equipment for schools and households as common information media for education and entertainment. Computer graphics helps to mass expand computers and remove the barriers that ordinary people experience when working with them. In this book, modern approaches, procedures, algorithms, as well as devices in the area of light and colors, shading and lighting, realistic and photorealistic imaging, definition of graphical scenes or objects, and security based on graphical objects are presented. Graphical transformations and projections, spatial imaging, curves and surfaces, filling and texturing, image filtering, and virtual reality are also covered.




Physically Based Rendering


Book Description

This updated edition describes both the mathematical theory behind a modern photorealistic rendering system as well as its practical implementation. Through the ideas and software in this book, designers will learn to design and employ a full-featured rendering system for creating stunning imagery. Includes a companion site complete with source code for the rendering system described in the book, with support for Windows, OS X, and Linux.




Three Dimensional Projection


Book Description

What is Three Dimensional Projection A 3D projection is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: 3D Projection Chapter 2: Cartesian Coordinate System Chapter 3: Spherical Coordinate System Chapter 4: Isometric Projection Chapter 5: Orthographic Projection Chapter 6: Rotation (Mathematics) Chapter 7: Oblique Projection Chapter 8: Transformation Matrix Chapter 9: Rotation Matrix Chapter 10: Vector Projection (II) Answering the public top questions about three dimensional projection. (III) Real world examples for the usage of three dimensional projection in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Three Dimensional Projection.